What Is Nash Equilibrium?

Nash equilibrium, also known as non-cooperative game equilibrium, is an important term in game theory, named after John Nash. In a game process, regardless of the opponent's strategy choice, one party will choose a certain strategy. This strategy is called dominant strategy. If the strategy combination of two game parties constitutes their respective dominant strategies, then this combination is defined as Nash equilibrium.

Nash equilibrium, also known as non-cooperative game equilibrium, is

The important results about the universal significance of the Nash equilibrium and the proof of the existence theorem, which lay the foundation for the development of non-cooperative game theory, are

Nash balance can be divided into two categories: "Pure strategic Nash balance" and "

The Nash equilibrium theory lays the fundamental foundation of modern mainstream game theory and economic theory, as Kreps (1990) stated in the introduction of "Game Theory and Economic Modeling", During the year, economics has undergone a moderate revolution in methodology, language, and concepts. Non-cooperative game theory has become the center of the paradigm ... in economics or financial, accounting, marketing, and political science related to economic principles. In other disciplines, it is now difficult for people to find areas that do not understand Nash balance and can 'consume' recent literature. "The important impact of Nash balance can be summarized as the following six aspects

1. Changed the system and structure of economics. The concepts, contents, models, and analytical tools of non-cooperative game theory have penetrated into most disciplines of economics such as microeconomics, macroeconomics, labor economics, international economics, and environmental economics, and have changed The content and structure of these subject areas have become the basic research paradigm and theoretical analysis tools of these subject areas, thus changing the connotation of each branch of the original economic theory system.

2. Expanded the scope of economic research on economic issues. The original economics lacked effective methods to model the uncertain factors, changing environmental factors, and interactions between economic individuals, so it was impossible to analyze the economic problems at the micro level. Nash equilibrium and related model analysis methods, including extended game method, inverse induction method, subgame perfect Nash equilibrium and other conceptual methods, provide economists with in-depth analysis tools.

3 Strengthen the depth of economics research. The Nash equilibrium theory does not evade the direct interaction between economic individuals, and is not satisfied with the simplification of the complex economic relations between economic individuals. When analyzing the problem, not only stay at the macro level, but also analyze the deep reasons and Law, emphasizing the discovery of the root of the problem from the perspective of the micro individual behavior law, so that economic problems can be understood and explained more deeply and accurately.

4 Formed a research paradigm system based on classic games. That is, various problems or economic relationships can be classified according to the types or characteristics of classic games, and researched according to the corresponding classic game analysis methods and models, and the experience gained in one field can be easily transplanted into another field.

5. Expand and strengthen the links between economics and other social and natural sciences. The Nash equilibrium is great because it's ordinary, and it's almost universal. The Nash equilibrium theory is applicable to the laws of human behavior, as well as the laws of survival, movement, and development of other organisms other than humans. The bridge effect of Nash equilibrium and game theory makes economics more closely linked with other social and natural sciences, and forms a virtuous circle in which economics and other disciplines promote each other.

6. Changed the language and expression of economics. The well-known Japanese economist Kandori Michihiro (1997) in evolutionary game theory quotes Paul Samuelson "You can even make a parrot a trained economy The scientist, because it has to learn only two words, that is supply and 'demand, once made a humorous extension, he said, "Now this parrot needs to learn two more words, that is Nash balance.